Senators are looking out for their local post offices as the chamber debates an overhaul of the financially troubled U.S. Postal Service. But soon they might have to consider just how local they’re willing to go.

Sen. Rand Paul (R-Ky.) has filed an amendment to the Postal Service overhaul bill currently on the floor that would limit post offices in the Capitol complex to two: one on the House side and one on the Senate side.

Post offices currently operate out of the Cannon, Rayburn, Longworth and Ford House office buildings as well as in the Capitol.

“If they’re going to require post offices to close … we should look here first. We shouldn’t be treated any differently as other states,” Paul spokeswoman Moira Bagley said. “If we’re closing in Kentucky, we should be looking to close here, too … and we have how many post offices within walking distance from each other here?”

Paul’s suggestion that the Postal Service should cut back on the number of outlets that it operates on the Capitol campus is one the agency has also pondered.

Last summer, the Postal Service included the Capitol, Cannon and Rayburn locations on its list of nearly 3,700 post offices around the country that were being evaluated for closures.

Shutdowns were slated to begin in January, but the agency agreed to postpone eliminations until May because the backlash was so great. Lawmakers suggested the Postal Service was being rash and fiercely pledged to protect their local post offices.

Many House Members at that time were protective of their Capitol Hill post offices, too.

“I think we’re rushing to do stuff rather than to sit down and come up with a total kind of plan that we can look at from an economic standpoint,” Rep. Edolphus Towns (D-N.Y.) said in early December.

Some lawmakers said the agency should be the one making those decisions — not Congress.

“I’m a big fan that the post office needs to do what’s in its financial best interest, and so I would support anything which is cost effective for them,” Rep. Darrell Issa (R-Calif.), a leader of the House’s Postal Service overhaul efforts, said of Paul’s proposal.

“One of the interesting things about we in the House and the Senate, for better or for worse, is that we’re very big users of postal still, and that should drive the decision process.”

Reps. Dan Lungren (R-Calif.) and Robert Brady (D-Pa.), the chairman and ranking member of the House Administration Committee, were noncommittal.

“The chairman supports the common objective of consolidating postal operations to reduce costs and will support whatever alternative yields the most sustainable model,” Lungren spokeswoman Salley Wood said Wednesday.

Brady’s staff said he was still evaluating the proposal.

Senators who are major players in the Postal Service overhaul bill that is on the floor this week did not respond to comments on Paul’s suggestion.

But it may be moot.

Majority Leader Harry Reid (D-Nev.) has taken procedural steps to block Senators from formally offering amendments while negotiators work out an agreement to reduce the number of proposals considered.

Paul’s amendment was one of more than 50 filed by Wednesday afternoon that Homeland Security and Governmental Affairs Chairman Joe Lieberman (I-Conn.) said Senate leaders and floor managers need to sort through.

“I think we can come to an agreement on a number of amendments, have a good open debate, both sides, and then pass this bill,” Lieberman said.

Niels Lesniewski contributed to this report. Please send tips to notebook@rollcall.com.